Learn: Self-weight from unit weight
Self-weight is a permanent action caused by the material itself. When a component has uniform unit weight, multiplying that unit weight by the actual material volume gives its total weight force.
What the formula is saying
Unit weight tells you how many kilonewtons one cubic metre weighs. Repeating that amount for every cubic metre is multiplication by volume; gravitational acceleration is already included in unit weight.
Read the symbols in plain language
- γ
- Unit weight
Weight force per unit volume, including gravity. Mass density in kg/m³ cannot be entered directly in a kN/m³ field.
kN/m³Use kN/m³ as the base unit shown here. γ is in kN/m³ and V is in m³, giving kN. Mass density in kg/m³ is a different input: it must first be multiplied by g and divided by 1000 to obtain kN/m³.
- V
- Volume
Volume. Use material-filled volume, excluding openings and voids that carry no material weight.
m³Cubic metres measure volume, or a first moment of area where explicitly identified.
- G
- Result to find
Self-weight from unit weight. The cubic-metre units cancel, leaving the total unfactored weight force.
kN
Sort out the units first
γ is in kN/m³ and V is in m³, giving kN. Mass density in kg/m³ is a different input: it must first be multiplied by g and divided by 1000 to obtain kN/m³.
Assumptions before calculating
The material has one representative uniform unit weight and the volume excludes voids not filled with that material. The result is an unfactored weight before any action combination.
This is a first-generation Eurocode teaching relationship or an explicitly simplified coefficient calculation. The numbers supplied here are exercise data, not a recommendation for any country. Check the adopted edition, relevant clause, National Annex, applicability conditions and all other limit states before any real design.
Let’s solve one together
Read the given values, follow each operation, then check what the result means.
Read the supplied values as one complete study case. Find G and explain the result in the stated output unit.
- γ · Unit weight
- 25 kN/m³
- V · Volume
- 2 m³
Identify the actual material volume
Use material-filled volume, excluding openings and voids that carry no material weight.
(2) = 2 m³Multiply by unit weight
The cubic-metre units cancel, leaving the total unfactored weight force.
(25) × (2) = 50 kN
Does this worked answer make sense?
Doubling material volume doubles weight. A zero volume gives zero force; positive material and volume must not produce a negative weight magnitude.
A second worked example — different values
A second case uses different data. Predict which way the answer will change, then calculate it without reusing the first answer.
- γ · Unit weight
- 24 kN/m³
- V · Volume
- 3.5 m³
Identify the actual material volume
Use material-filled volume, excluding openings and voids that carry no material weight.
(3.5) = 3.5 m³Multiply by unit weight
The cubic-metre units cancel, leaving the total unfactored weight force.
(24) × (3.5) = 84 kN
Now try your own values
Change a value or its unit. The same method will show your calculation, step by step.
Results update only when you calculate. The lesson example above stays unchanged.
Your turn — check your understanding
Solve this separate case yourself. Use only the values below; the two worked examples use different data. Give the requested result in the selected unit.
- γ · Unit weight
- 18 kN/m³
- V · Volume
- 2.4 m³
Find: Learn: Self-weight from unit weight
A hint, not the answer
Unit weight tells you how many kilonewtons one cubic metre weighs. Repeating that amount for every cubic metre is multiplication by volume; gravitational acceleration is already included in unit weight.
γ is in kN/m³ and V is in m³, giving kN. Mass density in kg/m³ is a different input: it must first be multiplied by g and divided by 1000 to obtain kN/m³.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Identify the actual material volume
Use material-filled volume, excluding openings and voids that carry no material weight.
(2.4) = 2.4 m³Multiply by unit weight
The cubic-metre units cancel, leaving the total unfactored weight force.
(18) × (2.4) = 43.2 kN
Avoid the common trap
Do not multiply by g again when γ is already a unit weight. Do not use gross external volume for a hollow component without accounting for its voids.
When this method applies — and when it does not
Finishes, services, reinforcement allowances, moisture and partitions may require separate contributions. This calculation neither chooses a material density nor converts a total force into an area or line load.
For study and understanding, not approval of a real structure, site operation or design. Apply the correct standard, National Annex and professional review to actual engineering work.
One idea understood. Keep going.
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Sources & further reading
References open in a new tab and explain the underlying principles. The teaching text and examples here are SimpleFlick’s own; the source organisations have not endorsed this calculator.
Reading focus: Self-weight from unit weight. Action-specific reading: EN 1991-1-1 for self-weight, EN 1991-1-3 for snow, and EN 1991-1-4 for wind. National and site data are not generated by this lesson.
Lesson updated: · Both examples and the separate practice case are checked against an independent high-precision numerical implementation. This verifies arithmetic for the stated model, not engineering certification.